Some Basic Results on Banach Dialgebras
O. J. Ogunsola
Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria.
A. O. Abdulkareem *
Department of Mathematics and Computer Sciences, University of Africa Toru Orua, Bayelsa, Nigeria.
I. E. Daniel
Department of Mathematics, Spiritan University, Nneochi, Abia State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
We define some basic terms in Banach dialgebras and give some examples of the complete normed dialgebras. Some results of Banach dialgebras which are analogues to Banach algebras in functional analysis were also established. It was proved that the differential associative algebra is a dialgebra if the square of the differential is an identity mapping. Condition under which the differential map is an isometric map is established. It was also proved that left and right products in Banach dialgebra are continuous. Finally, quotient of Banach dialgebra by its closed ideal is established to be a Banach dialgebra.
Keywords: Banach dialgebra, derivation, associative algebra